9.1- Rotation and Revolution
A key component in understanding the idea of circular motion is rotation, or when an object turns about an internal axis. An axis is a straight line around which rotation takes place. The reverse of rotation is a revolution, when an object rotates around an eternal axis. These three terms, rotation, revolution and axis are all important to understand when dealing with circular motion.
A skater rotates around an Axis
9.2 - Rotational Speed
Three values are judged when talking about rotational speed-
Linear Speed- simply the distance moved per second. The linear speed is always faster on the outside of the axis.
Tangential Speed- the speed of an object moving along a circular path. For circular motion, tangential speed and linear speed can be interchanged.
Rotational Speed- number of rotations per unit of time, or RPM (revolutions per minute)
Tangential Speed - the red arrow shows the direction the object would move if the object broke away from its orbit
Tangential speed = radial distance x rotational speed
At the center of a rotating object, there is no tangential speed, but there is rotational speed. The further away from the axis on a rotating object, the more the tangential speed increases. Rotational speed is constant throughout the rotating object, but the tangential speed varies.
9.3- Centripetal Force
Centripetal force is defined as any force that causes an object to follow a circular path. For example, when one swings a can on a string around their head, the only force acting on the can is directed inwards (neglecting gravity). Centripetal force depends on the mass, tangential speed, and radius of the circular path the object is moving in. It can be determined using the equation: F = mv²/r
m = mass v = tangential speed r = radius of curvature
9.4 - Centripetal and Centrifugal Forces
A centrifugal force is the polar opposite of centripetal force. Centrifugal force is not attributed to a force but to inertia. Thusly there is a tendency for any object being spun about, such as the can in the said example, to leave not away from the axis but on a tangential path to the circle.
9.5 - Centrifugal Force in a Rotating Reference
If something was inside a rotating object, it would feel centrifugal force acting on it similar to gravity. From the frame of reference outside the the rotating object, no centrifugal force would be visibly acting on the thing inside. Observation of centrifugal force depends on the reference point and is only the result of rotation, and not the result of two masses interacting like in gravitational forces. For this reason, physicists refer to centrifugal force as a ficticious force.
9.6 - Simulated Gravity
Gravity can be simulated by centrifugal force. For example, if there is a space station floating in space that is not rotating, the people on board feel weightlessness. However, if the space station rotated at the appropriate rate the crew would experience centrifugal force, which would feel like gravity.
Inside the space station, the acceleration experience is the centripetal/centrifugal acceleration due to rotation. The acceleration increases with increasing radial distance. Therefore, doubling the distance from the axis of rotation doubles the centripetal/centrifugal acceleration. At the axis, the radial distance is zero, so there is no acceleration because of rotation.
The smaller the diameter of the spinning object, the faster it has to spin to effectively simulate gravity.
Circular Motion
9.1- Rotation and Revolution
A key component in understanding the idea of circular motion is rotation, or when an object turns about an internal axis. An axis is a straight line around which rotation takes place. The reverse of rotation is a revolution, when an object rotates around an eternal axis. These three terms, rotation, revolution and axis are all important to understand when dealing with circular motion.
9.2 - Rotational Speed
Three values are judged when talking about rotational speed-
Tangential speed = radial distance x rotational speed
At the center of a rotating object, there is no tangential speed, but there is rotational speed. The further away from the axis on a rotating object, the more the tangential speed increases. Rotational speed is constant throughout the rotating object, but the tangential speed varies.
9.3- Centripetal Force
Centripetal force is defined as any force that causes an object to follow a circular path. For example, when one swings a can on a string around their head, the only force acting on the can is directed inwards (neglecting gravity).
Centripetal force depends on the mass, tangential speed, and radius of the circular path the object is moving in. It can be determined using the equation: F = mv²/r
m = mass v = tangential speed r = radius of curvature
9.4 - Centripetal and Centrifugal Forces
A centrifugal force is the polar opposite of centripetal force. Centrifugal force is not attributed to a force but to inertia. Thusly there is a tendency for any object being spun about, such as the can in the said example, to leave not away from the axis but on a tangential path to the circle.
9.5 - Centrifugal Force in a Rotating Reference
If something was inside a rotating object, it would feel centrifugal force acting on it similar to gravity. From the frame of reference outside the the rotating object, no centrifugal force would be visibly acting on the thing inside. Observation of centrifugal force depends on the reference point and is only the result of rotation, and not the result of two masses interacting like in gravitational forces. For this reason, physicists refer to centrifugal force as a ficticious force.
9.6 - Simulated Gravity
Gravity can be simulated by centrifugal force. For example, if there is a space station floating in space that is not rotating, the people on board feel weightlessness. However, if the space station rotated at the appropriate rate the crew would experience centrifugal force, which would feel like gravity.
The smaller the diameter of the spinning object, the faster it has to spin to effectively simulate gravity.
Sources
Conceptual Physics Third Edition with Expanded Technology, Paul G. Hewitt
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular%20Motion/Images/LinearVelAnim.gif
http://www.mansfieldct.org/schools/mms/staff/hand/lawsCentripetalForce_files/image004.jpg
http://www.worsleyschool.net/science/files/whichway/station.gif